“…Following this conversion, we applied the estimation model of the breakthrough time by Wood et al 21) . In this model, the service lives of cartridges or activated carbon beds for organic vapors are estimated by extension 21,[29][30][31][32][33][34][35][36][37][38][39][40][41][42][43] 1) where: t b = breakthrough time (min), W e = adsorption capacity of carbon (g/g-carbon), W = carbon bed weight (g), C 0 = challenge vapor concentration (g/cm 3 ), C = breakthrough concentration (g/cm 3 ), Q = airflow rate (cm 3 /min), ρ B = bulk density of carbon (g/cm 3 ), k v = adsorption rate coefficient (min -1 ). In the estimation, a single vapor is assumed to be the adsorbate, and the Dubinin-Radushkevich (D-R) equation (Equation 2) 44,45) is used to calculate the value of W e for individual organic vapors: (2) where: W 0 = micropore volume or adsorption space (cm 3 /g-carbon), d L = liquid density of adsorbate (g/cm 3 ), R = ideal gas constant (8.315 kJ · K -1 /mol), T = temperature (K), b OV = affinity coefficient of organic vapor (dimensionless parameter), E 0 = adsorption energy of a reference adsorbate (kJ/ mol), p sat = bulk liquid saturation vapor pressure at the temperature (kPa), p = pressure of vapor (kPa).…”